Directed harmonic currents for laminations on certain compact complex\n surfaces

2013/04/10 by Carlos Pérez-Garrandés, Pérez-Garrandés, Carlos
Mathematics · #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1304.3032

Abstract

Let \L be a Lipschitz lamination by Riemann surfaces embedded in\nM. If M is a complex torus, mathbbCP¹\× mathbbCP¹ or\n mathbbT¹\× mathbbCP¹ and there is no directed closed current then\nthere exists a unique directed harmonic current of mass one. Moreover if\n\L is embedded in M= mathbbCP¹\× mathbbCP¹ and has no\ncompact leaves, then there is no directed closed current. If \L is\nnot Lipschitz, then slightly weaker results are obtained.\n

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